This paper proposes a mechanism for imitating hand-object interactions like grasps, manipulations, etc. It is jointly based on neurophysiology and robotics. The aim of the mechanism is both the task goal and a reasonable degree of accuracy in the task itself. In addition, it addresses both the problem of how to imitate and when. The test platform consists of two simulated robots and an object that they interact with. The results presented here show both successful imitation of familiar actions and poor imitation of unfamiliar interactions. It is intended that this mechanism is used to control the movements of real robots that would imitate other robots or humans.